Subgroups — C₂×Dic₂₆₀₈ #35216841

Order 20864.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₀₄	C₂	1	2	yes	maximal
2	Dic₂₆₀₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₁₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₆₅₂	—	2	2	no	—
5	Dic₁₃₀₄	—	2	2	no	—
6	Dic₁₃₀₄	C₂²	1	4	yes	—
7	C₂×C₁₆×C₁₆₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₆₃	C₂²	1	2	yes	—
9	C₂×Dic₃₂₆	—	4	2	no	—
10	Dic₆₅₂	—	2	4	no	—
11	Dic₆₅₂	—	4	2	no	—
12	C₂×C₈×C₁₆₃	D₄	1	1	yes	characteristic
13	C₁₆×C₁₆₃	D₄	1	1	yes	characteristic
14	C₁₆×C₁₆₃	C₂³	1	1	yes	characteristic
15	Dic₃₂₆	—	4	4	no	—
16	Dic₃₂₆	—	8	2	no	—
17	C₂×Dic₁₆₃	—	8	2	no	—
18	C₂×C₄×C₁₆₃	D₈	1	1	yes	characteristic
19	C₈×C₁₆₃	D₈	1	1	yes	characteristic
20	C₈×C₁₆₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₁₆₃	D₁₆	1	1	yes	characteristic
22	C₄×C₁₆₃	D₁₆	1	1	yes	characteristic
23	C₄×C₁₆₃	C₂×D₈	1	1	yes	characteristic
24	Dic₁₆₃	—	8	4	no	—
25	C₂×C₁₆₃	Q₆₄	1	2	yes	complemented
26	C₂×C₁₆₃	C₂×D₁₆	1	1	yes	characteristic
27	C₁₆₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₆₄	—	163	1	no	maximal, Sylow
29	C₂×Q₃₂	—	163	2	no	—
30	Q₆₄	—	163	4	no	—
31	C₂×C₃₂	D₁₆₃	1	1	yes	characteristic
32	C₂×Q₁₆	—	326	2	no	—
33	Q₃₂	—	326	2	no	—
34	Q₃₂	—	163	4	no	—
35	C₂×C₁₆	C₂×D₁₆₃	1	1	yes	characteristic
36	C₃₂	C₂×D₁₆₃	1	2	yes	—
37	C₂×Q₈	—	652	2	no	—
38	Q₁₆	—	326	4	no	—
39	Q₁₆	—	652	2	no	—
40	C₂×C₈	D₆₅₂	1	1	yes	characteristic
41	C₁₆	D₆₅₂	1	1	yes	characteristic
42	C₁₆	C₂²×D₁₆₃	1	1	yes	characteristic
43	Q₈	—	1304	2	no	—
44	Q₈	—	652	4	no	—
45	C₂×C₄	—	1304	2	no	—
46	C₂×C₄	D₁₃₀₄	1	1	yes	characteristic
47	C₈	D₁₃₀₄	1	1	yes	characteristic
48	C₈	C₂×D₆₅₂	1	1	yes	characteristic
49	C₂²	D₂₆₀₈	1	1	yes	characteristic
50	C₄	—	1304	4	no	—
51	C₄	D₂₆₀₈	1	1	yes	characteristic
52	C₄	C₂×D₁₃₀₄	1	1	yes	characteristic
53	C₂	Dic₂₆₀₈	1	2	yes	direct product factor
54	C₂	C₂×D₂₆₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₆₀₈
commutator, cosocle	C₁₆×C₁₆₃	C₂³
Frattini	C₁₆	C₂²×D₁₆₃
Fitting	C₂×C₃₂×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	D₁₆
hypercenter	C₂×C₃₂	D₁₆₃
hypocenter	C₁₆₃	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₆₃ ▷ C₈×C₁₆₃ ▷ C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. Dic₂₆₀₈	C₂	direct (N × H)
25. C₂×C₁₆₃	Q₆₄	semidirect
27. C₁₆₃	C₂×Q₆₄	semidirect
53. C₂	Dic₂₆₀₈	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Dic₁₃₀₄	2
Dic₂₆₀₈	2
C₂×C₃₂×C₁₆₃	2
C₂×Q₆₄	163

Subgroups — C2×Dic2608 #35216841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₆₀₈ #35216841